Pasternak双参数地基上Euler-Bernoulli裂纹梁弯曲的解析解

Analytical Solution of Bending Deformation of the Euler-Bernoulli Cracked Beam on Pasternak Two-Parameter Foundation

基于开裂纹的等效扭转弹簧模型,采用Laplace变换,给出了Pasternak地基上具有任意裂纹数目的Euler-Bernoulli梁弯曲变形的解析通解.在验证本文解析解正确的基础上,数值分析了Pasternak地基上简支裂纹梁的弯曲变形和内力特征,考察了裂纹数目、深度、位置以及地基反力系数对裂纹梁弯曲的影响.结果表明:在裂纹处梁挠度分布存在尖点,而转角分布存在跳跃,并且尖点效应和转角跳跃随着裂纹深度的增加而愈加明显;同时随着地基反力系数的增大,裂纹梁的挠度、弯矩和转角逐渐减小;此外,随着地基反力系数的增大,裂纹数目对裂纹梁挠度的影响逐渐减弱.这些结果为Pasternak地基上梁的裂纹损伤识别提供了理论基础.

Based on the equivalent rotational spring model for the open cracks, an explicit analytical solution of the bending of Euler-Bernoulli beam with arbitrary number of cracks was presented on Pasternak foundation by using Laplace transform. On the basis of verifying the correctness of the analytical solution proposed in this paper, the bending deformation and internal force characteristics of simply supported cracked beams on Pasternak foundation were numerically analyzed. The influences of the number, depth and position of cracks and the foundation reaction coefficient on the bending of cracked beams were investigated. It was revealed that there exists, at the crack location, a cusp on the deflection curve and a jump on the rotational angle curve. The cusp and jump become more and more obvious as the crack depth increases. The deflection, bending moment and angle of the cracked beam gradually decrease as the foundation reaction coefficient increases. In addition, the effect of the number of cracks on the deflection of the cracked beam gradually decreases with the increase of the foundation reaction coefficient. These results provide a theoretical basis for the identification of crack damage in beams on Pasternak foundation.